NOTE. When the per cent. is expressed by a decimal of more than 2 places, the figures after the second decimal place must be regarded as parts of 1 per cent.; thus, (in the last line of the foregoing table,) .125 is 12% or 12 per cent. Ex. 1. Write the decimal for 4 per cent. Ans. .04. 2. Write the decimal for 8 per cent.; 12 per cent.; 16 per cent.; 25 per cent.; 72 per cent. 3. Write the common fraction for 163 per cent. ; 20 per cent. ; 33 per cent.; 75 per cent. 1st Ans. t. PROBLEM 1. 226. To find the percentage, the base and rate per cent. being given. Ex. 1. B had $175, but lost 8 per cent. of it; how many dollars did he lose? $175 $14.00, Ans. Since 8 per cent. is .08 = the loss is found by multiplying $175 by .08 or by Hence, RULE 1. Multiply the base by the per cent., written decimally; or, RULE 2. Find such part of the base as the rate is of 100 (Art. 151). 2. A farmer having 48 sheep, lost 25 per cent. of them; how many did he lose? 221. Meaning of per cent.? 222. Rate per cent.? 223. Percentage? 224. Base of percentage? 225. In what ways may the rate be expressed? If expressed decimally by more than two figures, what are the figures after the second decimal place? 226. Rule for finding percentage when the base and rate are given? Second Rule? 3. What is 6 per cent. of $250 ? 5. What is 12 per cent. of $500 ? Ans. $15. Ans. $62.50. 6. What is 83 per cent. of 600bush. of wheat? Ans. 50bush. 7. What is 163 per cent. of 1200 lb. of cheese? Ans. 2001b. 8. A farmer cultivates 25 acres of corn this year, and intends to cultivate 20 per cent. more next year; how many acres does he intend to cultivate next year? Ans. 30. 9. In an orchard of 900 trees, 331 per cent. are peach trees; how many peach trees are there in the orchard? 10. A teacher pronounced 56 words for his pupils to spell, but 14 per cent. were mis-spelled; how many words were misspelled? 11. Only 663 per cent. of a class of 27 pupils solved a problem given them for a lesson; how many of the class failed? 12. The population of a certain city is 18775, what will it be in one year from this time if it gains 8 per cent.? 13. The population of a certain State is 1376875, what will it be in one year if it loses 12 per cent.? 14. A and B commenced business, each with $8456. A gained 25 per cent. and B lost 12 per cent.; how much was A then worth more than B? 15. A speculator paid $56895 for a lot of flour, and lost 9 per cent.; for what sum did he sell the flour? 16. One acre of corn yields 80 bushels, and another acre 20 per cent. more; how many bushels does the second acre yield? PROBLEM 2. 227. To find the rate per cent. when the base and percentage are given. Ex. 1. One dollar is what per cent. of $4? 4) 100 2 5, Ans. One dollar is 4 of $4, and 4 reduced to a decimal is .25; i. e. $1 is 25 per cent of $4. The same result is obtained by multiplying $1 by 100, and dividing the product by 4. Hence, RULE. Multiply the percentage by 100, and divide the product by the base. NOTE. This rule is the converse of that in Art. 226; thus, 25 per cent. of $4 is $4 X .25 $1; and, conversely, $1.00 2. What per cent. of $150 is $18? 3. What per cent. of $300 is $19? $4 = .25, i. e. 25 per cent. 12 per cent., Ans. Ans. 63 per cent. Ans. 12 per cent. Ans. of 1 per cent. 8. B inherited $3500, and in 6 months spent $875; what per cent. of his inheritance did he spend? What per cent. had he remaining? Ans. Spent 25 per cent., and had 75 per cent. 9. Out of a cask of wine containing 96 gallons, 32 gallons were drawn; what per cent. of the whole remained in the cask? 10. A merchant having $1000, deposited $650 in a bank; what per cent. of his money did he deposit? 11. A teacher having a salary of $2400, spends $2000 annually; what per cent. of his salary does he save? PROBLEM 3. 228. To find the base when the percentage and the rate are given. Ex. 1. $6 is 3 per cent. of what sum? If $6 is 3 per cent., then 1 per cent. is of $6, which is $2, and if $2 is 1 per cent., then 100 per cent. is 100 times $2, which is $200; .. $6 is 3 per cent. of $200, Ans. The same result is obtained by first multiplying $6 by 100, and then dividing the product by 3; thus, $600 ÷ 3 = $200, Ans. Hence, RULE. Multiply the percentage by 100, and divide the product by the rate. 227. Rule for finding the rate when the base and percentage are known? What of this rule, and that in Art. 226? 228. Rule for finding the base when the percentage and rate are known? 2. $9 is 4 per cent. of what sum? Ans. $225. Ans. $1250. Ans. $171.429. Ans. 400. 9. A farmer bought a farm for $2756, which was 25 per cent. of his property; what was his property? Ans. $11024. 10. A man sold 56 geese, which was 28 per cent. of his flock; how many geese had he? 11. A merchant having a quantity of flour, bought 600 barrels more, when he found that the quantity bought was 75 per cent. of all he then had; how many barrels had he before he bought the last lot? Ans. 200. 12. A teacher saves $400 annually, which is 163 per cent. of his salary; what is his salary? 13. The population of a town was 769 greater in 1800 than in 1850, and this was an increase of 20 per cent. on the population of 1850; what was the population in 1850? 229. INTEREST. INTEREST is money paid for the use of money. The PRINCIPAL is the sum for which interest is paid. The AMOUNT is the sum of the principal and interest. 230. An example in interest is only a question in percentage. The principal is the base of percentage (Art. 224), the interest is the percentage (Art. 223), and the interest on $1 for a year is the rute written decimally (Art. 222). 231. The rate is usually fixed by law, and a higher rate than the law allows is usury. In New England and most of the United States the legal or lawful rate is 6 per cent.; in New York, 7 per cent.; in most of the Western States, as high as 10 per cent. by agreement; in Texas, as high as 12 per cent. ; in California, any rate by agreement, etc. On debts in favor of the United States, 6 per cent. In France and England, 5 per cent. NOTE. In this treatise, mentioned. per cent. is understood when no per cent. is of 6c.: = 5 mills 6 months, 3c.; 9 mill; for 2 days, m.; 6 days, 1m.; 24 days, 4m.; etc., 232. When the rate is 6 per cent., the interest of $1 for a year is 6c.; for 2 years, 12c., etc.; for 1 month, or c.; for 2 months, 1c.; 3 months, 14c.; months, 44c., etc.; for 1 day, 3 of 5 mills = m.; 3 days, m.; 4 days, m.; 5 days, 7 days, 14m.; 9 days, 14m.; 12 days, 2m.; Hence, etc. To find the interest of $1 at 6 per cent. for any time, RULE. Take 6c. (= $.06) for each year, 1c. for each 2 months in the part of a year, 5 mills (= $.005) for the odd month, if there be one, and 1 mill for each 6 days in the part of a month. Ex. 1. What is the interest of $1 for 3yr. 9m. 18d.? 2. What is the interest of $1 for 2yr. 5m. 20d.? 231. What will be understood when no rate is mentioned ? for finding the interest of $1 at 6 per cent. for any given time? 232. Rule |